Solve 3sqrt{6}*2sqrt{8}

$$3 \sqrt { 6 } \times 2 \sqrt { 8 }$$

Evaluate

$$24\sqrt{3}\approx 41.569219382$$

Solution Steps

Multiply 2 and 3 to get 6.

$$6\sqrt{6}\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$6\sqrt{6}\times 2\sqrt{2}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{6}\sqrt{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$12\sqrt{2}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$12\times 2\sqrt{3}$$

Multiply 12 and 2 to get 24.

$$24\sqrt{3}$$